I don't know that I agree with that--at least not in all cases. Most alcoholics DO have a desire to live--they just want to be able to live and drink.
In terms of alcoholism being devastating to one's health, and likely to result in an early death unless it is arrested, yeah--very dangerous. But "suicide" implies a wish to die, which isn't WHY alcoholics drink (though they may get to the point where they want to die).